New scaling model for variables and increments with heavy-tailed distributions

Monica Riva, Shlomo P Neuman, Alberto Guadagnini

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

Many hydrological (as well as diverse earth, environmental, ecological, biological, physical, social, financial and other) variables, Y, exhibit frequency distributions that are difficult to reconcile with those of their spatial or temporal increments, ΔY. Whereas distributions of Y (or its logarithm) are at times slightly asymmetric with relatively mild peaks and tails, those of ΔY tend to be symmetric with peaks that grow sharper, and tails that become heavier, as the separation distance (lag) between pairs of Y values decreases. No statistical model known to us captures these behaviors of Y and ΔY in a unified and consistent manner. We propose a new, generalized sub-Gaussian model that does so. We derive analytical expressions for probability distribution functions (pdfs) of Y and ΔY as well as corresponding lead statistical moments. In our model the peak and tails of the ΔY pdf scale with lag in line with observed behavior. The model allows one to estimate, accurately and efficiently, all relevant parameters by analyzing jointly sample moments of Y and ΔY. We illustrate key features of our new model and method of inference on synthetically generated samples and neutron porosity data from a deep borehole. Key Points: A new statistical scaling model is developed, explored and applied Apparent inconsistency between variable and increment statistics is eliminated Parameters are estimated using variable and increment moments jointly

Original languageEnglish (US)
Pages (from-to)4623-4634
Number of pages12
JournalWater Resources Research
Volume51
Issue number6
DOIs
StatePublished - Jun 1 2015

Keywords

  • heavy-tailed distributions
  • neutron porosity
  • parameter estimation
  • scaling
  • sub-Gaussian

ASJC Scopus subject areas

  • Water Science and Technology

Fingerprint Dive into the research topics of 'New scaling model for variables and increments with heavy-tailed distributions'. Together they form a unique fingerprint.

  • Cite this